How to find the limit of:
$\lim_{n\to\infty} \sqrt[n]{n+\sin^2n}$
using squeeze theorem?
Because $0\le \sin^2n \le 1 $, I find $a_n=\sqrt[n]{n}$ (which is equal to 1) and $c_n=\sqrt[n]{n+1}$, but I don't know how to prove that second formula is also a 1. Could someone help me solve it please? Thank you!